Question

A production manager needs to develop a production schedule to meet the following demand:

Period	1	2	3	4	5	6
Demand	600	600	800	1000	1200	600

Productions costs are as follows: (a) regular time: $3 per unit. (b) over-time: $5 per unit. (c) subcontract: $7 per unit. (d) Inventory carrying cost = $2 per unit per period (e) Back-order costs = $5 per unit per period.

Suppose some workers have retired, and the regular production rate can be only 700 units per period. Further, no subcontracting is allowed. However, it is possible to schedule production on an over-time basis

.

Answer 1

We can calculate the cost in 2 scenarios:

Scenario 1 - No inventory carried forward. Inventory produced to meet demand with over-time hours

Scenario 2 - Inventory carried forward. Inventory produced with over-time hours only for differential to demand

Subcontract cost is not relevant since subcontracting is not allowed.

Back-order cost is not helpful since demand is with gradual increase and can only be fulfilled by overtime.

Scenario 1 - No inventory carried forward. Inventory produced to meet demand with over-time hours

Period	1	2	3	4	5	6	Total
Demand	600	600	800	1000	1200	600	4800
Regular Production	600	600	700	700	700	600	3900
Overtime Production	0	0	100	300	500	0	900
							4800
Regular Time Rate	$           3	$           3	$           3	$           3	$           3	$           3
Regular Cost	$    1,800	$    1,800	$    2,100	$    2,100	$    2,100	$    1,800	$ 11,700
Regular Time Rate	$           5	$           5	$           5	$           5	$           5	$           5
Regular Cost	$         -	$         -	$       500	$    1,500	$    2,500	$         -	$    4,500
Total Cost	$    1,800	$    1,800	$    2,600	$    3,600	$    4,600	$    1,800	$ 16,200

Scenario 2 - Inventory carried forward. Inventory produced with over-time hours only for differential to demand

Period	1	2	3	4	5	6	Total
Demand	600	600	800	1000	1200	600	4800
Inventory Balance C/F	100	200	100	0	0	0	400
Regular Production	700	700	700	700	700	600	4100
Overtime Production	0	0	0	200	500	0	700
							4800
Regular Time Rate	$           3	$           3	$           3	$           3	$           3	$           3
Regular Cost	$    2,100	$    2,100	$    2,100	$    2,100	$    2,100	$    1,800	$ 12,300
Regular Time Rate	$           5	$           5	$           5	$           5	$           5	$           5
Regular Cost	$         -	$         -	$         -	$    1,000	$    2,500	$         -	$    3,500
Carrying Cost Rate	$           2	$           2	$           2	$           2	$           2	$           2
Carrying Cost	$       200	$       400	$       200	$         -	$         -	$         -	$       800
Total Cost	$    2,300	$    2,500	$    2,300	$    3,100	$    4,600	$    1,800	$ 16,600

Based on the above calculations, Scenario 1 has lesser cost and is preferable.